Twisted Koecher-Maass series of the Ikeda type lift for the exceptional group of type $E_{7,3}$

TL;DR

This paper computes twisted Koecher-Maass series for the Ikeda lift on the exceptional group E_{7,3} and establishes their rationality, advancing understanding of automorphic forms on exceptional groups.

Contribution

It provides explicit calculations of twisted Koecher-Maass series for the E_{7,3} Ikeda lift and proves their rationality, a novel result in the theory of automorphic forms on exceptional groups.

Findings

Explicit formulas for twisted Koecher-Maass series of the Ikeda lift.

Proof of rationality for these series.

Enhanced understanding of automorphic forms on E_{7,3}.

Abstract

We compute the twisted Koecher-Maass series of the first and second kind of the Ikeda type lift for the exceptional group of type $E_{7,3}$. As an application, we obtain their rationality result.